Linear \evol{} refers to update contexts with at most one bullet (hole).
Notice: this encoding works (maybe) only for the linear version of \evol{}


\begin{eqnarray*}
\encp{P \parallel Q}{s} & = & \encp{P}{s} \parallel \encp{Q}{s}\\
\encp{P + Q}{s} & = & \encp{P}{s} + \encp{Q}{s}\\
\encp{! P}{s} & = & ! \encp{P}{s}  \\
\encp{\alpha.P }{s} & = & s.\alpha.\encp{P}{s}  \textrm{ with } \alpha = a \mid \outC{a} \\
\encp{\bullet}{s} & = & \outC{x}  \\
\encp{\update{a}{P}.Q}{s} & = & a(x). ( \encp{P}{s} \parallel \encp{Q}{s} )   \\
\encp{\component{a}{P}}{s} & = & 
\textrm{sol 1: } (\nu l,l_a)( la.\outO{a}{l_a} \parallel \outC{l_a} \parallel !l_a.l.\outC{l_a} \parallel \encp{P}{s.l}  )\\ 
& = & 
\textrm{sol 2: } (\nu l,l_1,l_2)( \outO{a}{l_2} + \outC{l_1}) \parallel  \parallel !l_1.l.(\outO{a}{l_2} +\outC{l_1}) \parallel !l_2.l.\outC{l_2}  \parallel \encp{P}{s.l}  )
\end{eqnarray*}

Remarks: 
$\encp{P}{} = \encp{P}{\epsilon}$ where $\epsilon$ is the empty sequence 

$s$  is a sequence of inputs. 

Regarding solution 1 and solution 2: I think they are equivalent (in this case sol 1 is shorter) but i am not sure and then i think solution 2 is the one that should be correct